Time-frequency analysis of intermittent coherent structures in turbulent flows

Time-frequency analysis is a popular and powerful tool for identifying and analyzing intermittent events in fluid systems. Typically, these analyses are carried out by computing spectrograms or scalograms from the time history of a single flow variable at a single location in space, e.g., one component of velocity at some location of interest. A disadvantage of this approach is that the relationship between spectrograms or scalograms computed at different points in the flow or for different flow quantities is ambiguous, and, in particular, the role of coherent structures in producing the observed intermittency is obscured. In this presentation, we introduce an approach for generating global spectrograms and scalograms that describe the time-frequency behavior of coherent structures defined over all flow variables and spatial locations. The method is based on two extensions of spectral proper orthogonal decomposition, which defines flow structures that evolve coherently in space and time (Towne et al., J. Fluid Mech. Vol. 847, 2018). We demonstrate the method using the example of coherent wavepacket structures in a turbulent jet.